48. 非均匀天线阵列与可移动天线

欢迎来到无线未来。

Welcome to Wireless Future.

我是埃米尔·比尔纳松，和往常一样，我和埃里克·拉尔森在一起。

I'm Emil Bjarnson, and as always, I'm here with Erik Larsson.

你今天怎么样？

How are you today?

你好，埃米尔，很好。

Hello Emil, good.

你呢？

How are you?

我很好。

I'm great.

今天我期待和你聊聊天线阵列。

And I'm looking forward today to talk to you about antenna arrays.

在你看来，什么是天线阵列？

So what is an antenna array to you?

当然，埃米尔。

Absolutely, Emil.

所以是天线。

So antennas.

首先，天线可以是很多不同的东西。

Well, to start with, an antenna could be a lot of different things.

我的意思是，在教科书里它可能只是一个小小的线条或符号，但现实中，它可能是单极子、偶极子，更常见的是贴片天线。

I mean, in the textbook it's just a little dash or something in the figure, but in reality, of course, it could be monopolar, dipolar, more commonly a patch antenna.

当我们提到天线阵列时，意思就是多个天线以某种方式排列在一起。

And then when we speak of antenna arrays, then we simply mean antennas that sit together in some arrangement.

它们可以像这样成对排列，或者基本上可以是任意数量。

So they could sit like, it could be two of them like this, or it could be any number basically.

天线阵列本身可以具有任何几何形状。

The antenna array itself could have whatever geometry.

最常见的是天线排列成线性阵列，沿着一条直线均匀分布。

The most common is that the antenna sits in a linear array and then they simply space along a straight line.

通常情况下，间距是均匀的，而且通常间距为半波长，这背后有很好的原因。

It's very common that the spacing is uniform and it's also very common that the spacing is half a wavelength, for good reasons.

但还有许多其他类型的天线阵列。

But there are lots of other kinds of antenna arrays.

例如，可以构建平面阵列，这些天线通常排列在一个平面板上，间距均匀，但也不一定如此。

For example, one can build planar arrays and then they all sit on a planar slab typically with uniform spacing but not necessarily so.

这些天线安装在RAID上，协同工作，这一概念也是现代电信和无线标准物理层的基础，特别是在5G中，所使用的天线阵列技术被称为大规模MIMO，而埃米尔正是这一领域的先驱，并撰写了大量论文和教材。

These antennas sit on the RAID and they all cooperate and act together, which is a concept that also underpins much of the physical layer in modern telecom and wireless standards, specifically in five gs, where the antenna array technology that's used goes under the name massive MIMO, which Emil has been a pioneer within and also written a lot of papers and textbooks.

也许你可以接过来，向观众简单介绍一下大规模MIMO。

Maybe you want to take over and tell the audience a little bit Massive MIMO specifically.

没错，我可以讲，尽管我觉得你在这一领域比我还更像先驱。

Right, I can do that, even if I think you as much of a pioneer in that topic than I am.

但确实，与使用一个非常大的天线相比，使用天线阵列的一个优势是，除了占据一定面积以收集更多能量——通常面积越大，天线能收集的能量就越多——你还希望更细致地感知周围环境。

But yeah, I think one aspect to the whole thing with having antenna arrays as compared to having one very huge antenna is that in addition to filling a particular area so that you can collect more energy, typically the more area you have, the more energy you can collect with your antennas, you also want to be able to observe the world more carefully.

因此，在大规模MIMO系统中，我们的理念是拥有大量的天线。

So in massive MIMO systems, the idea is that we have an abundance of antennas.

与某些东西相比，我们拥有非常多的天线，在这种情况下，是相对于同时在同一频率下向不同方向发送的数据流或不同波束的数量而言的。

We have very many antennas compared to something, in this case compared to the number of data streams or different beams, signals we send at the same time, at the same frequency, in different directions.

因此，天线的数量应该大于用户数量。

So the number of antennas should be greater than the number of users.

这种设计既有理论上的原因，也有实际的原因。

And there are theoretical reasons for this and there are practical reasons for this kind of design.

但一种理解方式是，当你拥有一个天线阵列时，可以将信号发送到不同方向，这就像将信号瞄准棋盘上的不同格子。

But one way to view it is that when you have an antenna array, you can send signal different direction and that's like aiming signals towards different squares on a chessboard.

如果棋盘上你剩下的棋子数量相对于格子总数来说很少，那么如果你随机放置它们，彼此发生碰撞的风险就很小。

And then if the number of pieces that you have left on your chessboard is relatively small compared to the number of squares you have have there, then there is a small risk that if you just put them out randomly, some of them will collide with each other.

每颗棋子之间最好有足够的空间，这样更容易将聚焦的信号发送给它们。

There should be a good chance that there is some space between each piece, and that makes it easier for you to sort of send focused signals towards them.

这就是汤姆·罗塞塔在提出这一概念时所称的 Massive MIMO。

And this is what Tom Rosetta was calling massive MIMO when he sort of invented this idea.

如今在5G系统中，我们通常的基站配备约64根天线，同时最多服务8个用户。

And nowadays in five gs, we typically have base station with some 64 antennas and we have eight users at most that we are serving at the same time.

所以你的意思是，我们在这阵列中拥有这么多天线，它们可以协同工作，形成波束，从而将一个波束对准第一个用户，另一个波束对准第二个用户，依此类推。

So basically you're saying we got all these antennas in the array and they can act coherently together so as to form beams so that we can shoot one beam at the first user, a different beam at the second user and so on.

然后我们只需要确保——当然也希望运气不错——这些用户彼此不要离得太近，以免波束相互干扰。

And then we just gotta make sure and and with with some luck, hopefully, that these users aren't too close to each other so that the beams don't collide.

你刚才说有64根天线。

You said 64 antennas.

我以前以为主流厂商的产品线中，大规模MIMO设备用的是128根。

I used to think it was a 128 in the main vendor product line massive MIMO units.

到底是64根，还是别的数目？

Is that 64 or is it something else?

实际上，64是他们所拥有的最大天线数量。

Actually 64 is the maximum number of antennas that they have.

他们也有32根天线的产品。

There are 32 products as well.

还有一点需要注意的是，有时他们提到的是实际存在的单元数量。

Then one should keep in mind that sometimes they are mentioning the number of elements that exists.

比如你刚才提到的那些贴片单元，就属于这类组成部分。

These are, for example, the patches that you are mentioning.

所以我们所说的一根天线，实际上可能由多个单元组成，这些单元协同工作以形成特定的方向特性。

So one antenna, as we call them, might actually consist of multiple elements that just act together in order to form a particular directivity.

不过这就牵扯到更多天线设计层面的内容了。

But that's more going into the antenna design.

我明白了。

I see.

所以你的意思是，最终会有64路数字或射频流被数字化并进行处理，是这样吗？

So you're saying that there are like 64 digital or RF streams that eventually get digitized and then processed.

对的。

Right.

所以当我们这些通信或信号处理领域的人员讨论天线时，我们的视角是：在设计信号和接收信号的过程中，我们在计算机里能够调控哪些量。

So when we as communication or signal processing people are talking about antennas, we are viewing it from what is it we can control in our computer when we are designing the signals and when we are receiving the signals.

而在电磁层面实际发生的情况，可能会让硬件设计中的阵元数量有所增加。

And then what's actually going on in the electromagnetics might potentially expand the number of elements somewhere in your hardware design.

这仅仅是为了填满你可以放置元件的空间。

That's just in order to fill the space where you can put out your elements.

当然。

Sure.

但我觉得有趣的问题是，有多少个数字流可以同时输入到这个阵列中。

But I mean, I feel the interesting question is how many digital streams, how many parallel digital streams can get fed to the array simultaneously.

据我理解，这个产品中就是64个。

And that will be 64 then in this product, as I understand you.

当人们刚开始研究这种MIMO技术时，它被称为空分多址，因为不同用户位于不同的空间位置，同时进行通信；如今，人们常提到多用户MIMO，其中MIMO代表多输入（即一侧的天线）和多输出（即另一侧的用户）。

And when people started to work with this type of MIMO technology, it was either called space division multiple access because you were having different users at different spatial locations and certain at the same time, nowadays people often talk about multi user MIMO, where MIMO stands for this multiple input that is the antennas on one side and multiple outputs that are the users on the other side.

在最初，人们认为，好吧，你有一定数量的天线。

And yeah, in the beginning, people were thinking that, okay, you have a certain number of antennas.

正如你所说，数字流的数量就是你能服务的最大用户数，等于天线的数量。

This is the number of digital streams, as you were saying, the maximum number of users you could serve is equal to that number of antennas.

当然，你希望尽可能多地发送信号。

And you of course want to send as many signals as you could.

从理论上讲，这确实是一个极限。

And in theory, that is kind of limit.

但事实上，要发送与天线数量相等的数字流非常困难，因为这样所有信号都会相互干扰，很难实现。

But then it turned out that it is in practice very hard to send as many digital streams as you have antennas because then everything will collide and it will be very hard to build this.

因此，托马斯·罗塞塔在2010年左右提出了大规模MIMO系统，其思路是构建一个系统，发送的数流少于天线数量，但依靠天线的冗余来实现这一目标。

This is why Tom Rosetta was coming up in around 2010 with his massive MIMO setup, when you are building the whole system in order to send fewer data streams than you have antennas, but and have this abundance of antennas to achieve this.

对。

Right.

当然。

Sure.

所以，这里的直觉应该很清楚，对吧？

So I mean, the intuition there should be clear, right?

你希望实际形成的波束远少于天线数量吗？

Do you want a lot more antennas than actual beams that you form?

因为如果你形成太多波束，它们相互冲突的可能性就会增加。

Because if you form too many beams, then the likelihood that some of them will collide goes up.

64根天线，你刚才说能同时形成八个波束？

That 64 antennas and did you say eight simultaneous beams that you could form?

是的。

Yeah.

我的意思是，64根听起来并不多。

I mean 64 doesn't sound that much to me.

我原本以为至少要有几百根，但也许未来我们会达到那个水平。

I would expect at least a few 100, but maybe in the future we will be getting that.

所以现在有了大规模MIMO技术，其理念是拥有比当前实际发射的波束多得多的天线单元。

So now with with massive MIMO technology, the idea is to have a lot more of antenna elements than beams that you actually shoot at the given time.

但你还需要知道这些波束应该朝哪个方向发射。

But you also need to know in what directions to shoot these beams.

在通信理论中，这被称为获取信道状态信息。

And that's what in comm theory we call having channel state information.

对我来说，真正让大规模MIMO如此出色的原因是，可以通过利用电磁互易性来获取这种信道状态信息，让每个终端都发送一个导频信号。

And to me, really what makes massive MIMO work so wonderfully is that this channel state information can be obtained by exploiting electromagnetic reciprocity so that each and every terminal sends a pilot waveform.

这个导频信号由阵列中的每个天线接收。

This pilot waveform is received at the array by each one of the antennas.

然后每个天线估计终端的信道冲激响应。

Then each one of the antennas estimates the channel impulse response terminal.

通过互易性，我们知道这个响应在上行和下行链路中是相同的。

Then by reciprocity we know that this response is the same in both directions to the same on uplink and on downlink.

然后可以利用这些信息来计算如何在下行链路中发射这些波束。

They can be used then to compute how to shoot these beams on the downlink.

是的。

Yes.

所以，你把大规模MIMO和这种互易性方法联系在一起，对吧？

So Yeah, so you associate massive MIMO with this reciprocity approach, right?

当然，100%。

Oh, 100%.

我的意思是，对我来说，大规模MIMO意味着两件事。

I mean, to me massive MIMO means two things.

第一，服务天线数量过剩。

Number one, an excess of service antennas.

因此，基站的天线数量大约是同时发射波束数量的五倍甚至十倍。

So on the order of five or maybe 10 times as many antennas at the base station as you shoot beams that you shoot simultaneously.

第二，利用互易性获取信道状态信息。

And number two, reciprocity to get channel state information.

对。

Right.

我认为这确实是构建系统的理想方式。

And I think this is certainly the ideal way of building things.

但也存在一些MIMO系统工作在无法使用你所描述的互易性方法的场景中。

Then there are MIMO systems operating in situations where you can't use reciprocity methods that you were describing.

其中一个具体原因可能是，你在向下传输给用户时使用一个频段，而在用户向上发送到基站时使用另一个频段。

And one particular reason for this might be that you have one frequency band when you're transmitting down to the users and one other frequency band where you are transmitted from the users up to the base station.

因此，你无法真正利用互易性。

So then you can't really utilize reciprocity.

不，没错。

No, that's right.

所以你是说TDD操作？

So you mean FTD operation?

我的意思是，

I mean,

我刚才说的互易性当然主要适用于TDD操作，即在时间上复用上行和下行链路。

what I said about reciprocity of course applies mainly to TDD operation where you duplex uplink and downlink over time.

当然，但在FDD中，情况就有点不同了。

Sure, but in FDD the story is a little different.

互易性不成立，因此需要其他技术来获取信道状态信息。

Reciprocity doesn't hold, so other techniques are needed to get this chance that information.

是的，当有很多用户在城市等复杂区域快速移动时，通信信道会迅速变化，而在无法使用互易性的系统中处理这种情况会非常困难。

Yeah, and then it will be a difficulty to have a lot of users that are moving around quickly in a complicated part of the world, in the city, for example, where there are very quick variations in the communication channels, and do this in a system where you can't use reciprocity.

因为，如果要在这些场景中工作，通常需要系统更简单一些，比如用户移动速度不快，这样就有更多时间来估算信道，或者环境具有某些简单特性，比如存在直视路径（LOS）信道，基站能直接看到用户，那么信道在频域上的变化就不会那么快。

Because, yeah, if you wanted to work in those situations, typically you need something to be a little bit simpler, such that people are not moving very quickly, so you have more time to figure out the channels or that the environment have some simple features such as you have a so called line of sight channel where the base station sees the user directly and then the channel is not varying as quickly over the frequency domain.

没错。

That's right.

我的意思是，当然。

I mean, sure.

我的意思是，如果你的所有用户都在视距范围内，原则上只需要

I mean, you got line of sight to all your users, then in principle it'd

估计角度，也许还有仰角，就能确定用户的位置，这就够了。

be enough to estimate the angle, maybe the elevation and estimate to the users, and that would be it.

我的意思是，你不需要从阵列中的每个天线单元获取完整的冲激响应。

I mean, you wouldn't need the complete impulse response from every antenna element in the array.

可能还有其他方法可以替代互易性来获取这些信道状态信息。

There might be other ways that could compete with reciprocity to get this channel state information.

我想和你聊聊埃米尔，关于天线阵列本身，它的样子，特别是它的拓扑结构，以及如何在阵列中布置天线。

Want to talk to you Emil about the antenna array itself, and what it looks like, and specifically its topology, and how to place the antennas within the array.

因为据我了解，主流5G设备供应商的主要5G产品中，这些面板都是矩形面板，上面均匀分布着小型贴片天线。

Because to my understanding in the main five gs products from the leading five gs equipment vendors, these panels are all like rectangular panels with small patch antennas that sit uniformly spaced on the grid.

你最近发表了一篇题为《从天线富足到天线智能：六代Gigantic MIMO系统》的论文。

And you have recently published a paper entitled From antenna abundance to antenna intelligence in six gs Gigantic MIMO systems.

在这篇论文中，你探讨并质疑了天线在面板上均匀分布在矩形网格中的这一设计假设。

Where you explore or really question this design assumption, question this design concept where antennas sit uniformly spaced in a rectangular grid on a panel.

那么，我们为什么要采取其他方式呢？

So why would we want to do anything else?

没错，这是个好问题。

Right, that's a good question.

我们的出发点其实是你之前提到的：为什么我们的系统中不使用更多的天线？

And the starting point was really what you alluded to earlier that why don't we have more antennas in our systems?

为什么我们不使用数百根天线？

Why don't we have hundreds of antennas?

如果我们回溯一下历史，在四代系统中，通常只有两到四根天线。

And if we look back a bit in time, then in the four gs system, there were typically two to four antennas.

而现在，五代系统中已经有了32根或64根天线。

And now we have 32 or 64 antennas in five gs.

如果我们继续以类似的方式扩展，下一代系统中将会有数百根天线。

And if we continue scaling in similar manners, we will have hundreds of antennas in the next generations.

但增加这些额外天线的原因是什么？

But what is the reason for adding these extra antennas?

这是因为你想发射更多的波束，从而同时服务更多用户。

Well, it is because you want to shoot more beams so we can serve more use at the same time.

但如果我们拥有的天线数量是所发射波束的四到八倍，那么为了服务更多用户，所需的天线数量会迅速增长。

But if we then have some four or eight times more antennas than we are sending beams, then the number of antennas that we need is growing very rapidly with the number of use we want to serve.

于是我开始思考，我们是否可以找到一种方法，在未来系统中依然能服务更多用户，但不需要那么多天线，也不必让天线数量增长得那么快，从而保持天线与波束数量之间四倍、八倍、十倍的比例关系。

And I started to think about, could we do something where we could still serve more antennas in future systems, but maybe not need as many as or scale the antennas as quickly so that we keep this kind of four, eight, 10 times more antennas than users.

是的。

Yeah.

我的意思是，如果我们希望同时发射更多波束，就需要更多天线来维持大规模MIMO系统中天线数量与波束数量之间的比例。

I mean, totally, if we want to shoot more beams simultaneously, we want more antennas to maintain this massive MIMO ratio between number of antennas and number of beams that we shoot.

但难道不是也因为我们需要更多天线来获得更好的链路预算吗？

But isn't it always also that we want more antennas to get a better link budget?

因为上行链路上的天线越多，就会吸收越多的功率。

Because the more antennas on uplink, the more power it will soak up.

在下行链路上，天线越多，就能形成越尖锐的波束，从而获得更好的链路预算或更高的信噪比。

On downlink, the more antennas, the sharper beam we can form, and the better link budget we can get or the better SNR.

所以这里增加天线数量确实有两个原因。

So there are really two reasons to increase the number itself here.

对。

Right.

这当然是对的。

That's certainly the case.

而且通常情况下，对于发送下行信号的基站，法规会限制特定方向（比如天线阵列垂直指向的主方向）上的信号强度上限。

And it's often so also that a base station that is transmitting the downlink, there is a regulation on how strong is the signal allowed to be in a particular direction, which is like the main direction pointing perpendicularly from your antenna array.

在构建天线阵列时，你需要确保能够达到最大允许值，以便为系统提供最远的覆盖范围。

And when you're building your array, you want to make sure that you can reach the maximum value in order to provide the longest coverage in your system.

但决定这个最大值的因素有很多。

But there is a number of different factors that is determining that maximum value.

这是你拥有的总发射功率。

It is the total transmit power you have.

这是你所使用的天线数量。

It is the number of antennas that you're using.

还有各个天线的增益和方向性。

And it's the sort of gain, the directivity on the individual antennas.

所以如果我们稍微减少天线数量，就需要通过增加总功率，或者调整天线增益来补偿。

So if we are cutting down on the number of antennas a little bit, then we will have to compensate by increasing the power in total or, yeah, just play with gain of the antenna.

因此，有多种方法可以维持链路预算。

So there are ways of maintaining the link budget.

是的，当然。

Yeah, sure.

当然，这种相互影响存在。

Of course, that sort of interplay there.

但无论如何，让我们聚焦于天线阵列本身的拓扑结构。

But at any rate, let's focus on the topology of the array itself.

也许我们先从基础开始。

And maybe to start with, let's get back to basics.

如果我们构建一个天线阵列，比如说它可以

If we build an antenna array, let's say it could

可以是任意形式，可以是平面的，可以是线性的，也可以是其他任何形式。

be whatever, could be a planar, could be a linear, could be anything.

假设它是一个线性阵列。

Let's say it's a linear array.

天线的位置真的有影响吗？

Does it really matter where the antennas are located?

对于给定的孔径，比如说我能够负担一个半米长的孔径，并且可以使用10个天线。

So for a given aperture, so let's say I can afford an aperture of whatever, half a meter long, and I can afford 10 antennas, let's say.

这些天线的放置位置真的重要吗？

Does it really matter where I place these antennas?

我的意思是，传统观点认为它们应该间隔半个波长。

I mean, conventional wisdom is that they should be spaced half a wavelength apart.

但这有关系吗？

But does this matter?

它们可以更稀疏、更密集，或者随机分布吗？

Could it be, like, spaced more sparsely or more densely or just randomly?

还是说这会产生影响？

Or does this make a difference?

对。

Right.

这取决于你希望通过这个天线阵列实现什么目标。

So it depends on what you want to achieve with this antenna array.

如果我们从最基本的功能开始，你希望从这个天线阵列向某个位置的用户发送信号。

So if we start from the most basic feature, you want to transmit from this antenna array to one user located somewhere.

那么你首先要确保天线具有一定的方向性，即在某些方向上比其他方向更优先。

Then the first thing you want to make sure is that your antennas are sort of they typically have some directivity, some directions that it prefers compared to others.

然后你希望将这种方向性大致对准用户，避免它们朝向错误的方向。

And then you want to aim that directivity roughly towards the user so they don't look away.

然后，你需要做的是，从每个天线发射相同的信号，但对它们进行不同的延迟或相位偏移，使得这些信号在到达接收端时能够同相叠加。

And then what you want to do is that the signal from each of the antennas, you transmit the same signal, but you delay them or phase shift them differently so that they are reaching the receiver in phase with each other.

所以它们在发射时不需要同相，只需要在接收时同相即可。

So they don't need to be in phase when it transmitted, it should be in phase when received.

但除此之外，只要你只是希望信号能到达用户，天线的排列方式可以是任意的。

But apart from that, you can have any arrangement of the antennas when you only want them to be reaching the user.

这基本上就是我们所说的波束成形。

And this is basically what we call beamforming.

我们发送相同的信号，但施加不同的相位偏移，它们叠加在一起，从而在接收端方向上形成一个波束。

We send the same signal with different phase shifts, they add up, and that is basically creating a beam over there aiming towards the receiver.

完全正确。

Absolutely.

是的。

Yeah.

所以在你被允许放置天线的这个区域内，天线的布局方式其实并不重要。

So that's a situation where it really doesn't matter how you put out the antennas in this area where you're allowed to have them.

当然。

Sure.

因为说到底，波束成形的关键在于接收端的信噪比和链路预算，而这仅取决于我们拥有的天线数量，因为它们会以正确的相位协同叠加，幅度因此相加。

Because I mean, with beamforming, basically what matters is the signal to noise ratio at the receiver, the link budget to the receiver, and that will be dependent only upon the number of antennas that we have, because they all act coherently together, so the amplitudes add up with a proper phase.

但在实际应用中，这里还需要考虑其他因素。

Now in practice, there will be other considerations also to make here.

首先，当然是元件之间的互耦。

One, of course, will be mutual coupling among the elements.

你大概不希望

You probably don't want

通常来说，把天线元件放置得比半波长更近。

to put antenna elements closer than half a wavelength, generally speaking.

是的，没错。

Yeah, exactly.

所以这就是为什么半波长这个说法的由来：如果你把它们放得太近，它们就会开始强烈地相互产生电磁干扰。

So that is one reason where this half a wavelength thing comes from, that if you put them close to each other, they start to electromagnetically interact a lot with each other.

然后，我整个例子中关于信号可以被传输并直接相加的假设可能就不成立了。

And then it might be that yeah, my whole example of sort of the signals can transmitted and just added up.

它们彼此之间是相对独立的。

They're acting sort of independent of each other.

这种假设就会被打破。

That kind of assumption breaks.

而这种情况通常会更糟，但也可能更好。

And then it's typically worse, but it could be better.

但我们先不深入讨论耦合的细节，只要保持间距大于半波长即可。

But let's not go into the details on on the coupling, but stay away so you are further away than half a wavelength.

是的，如果它们之间的距离更远，或者至少保持半波长的间距，那么耦合就是可控的，至少不会对天线阵列的性能造成不利影响。

Yeah, so if they sit further away or at least half a wavelength apart, then coupling is manageable and at least not a detrimental factor to the array performance.

那么，为什么通常天线阵列都采用半波长的间距呢？

So how is it then that typically arrays are built with half a wavelength of spacing?

我的意思是，我们刚刚已经达成共识，从链路预算或接收端信噪比的角度来看，它们的摆放位置其实并不重要。

I mean we just agreed that from a link budget perspective or from an SNR at the receiver point of view, it doesn't matter where they are placed.

所以

So

那么，为什么当今的典型设计都基于半波长或λ/2的间距呢？

how is it then that typical designs of today are built upon a lambda half or half wavelength spacing.

对。

Right.

这涉及到当你同时处理多个用户或多个数据信号时的其他考量。

So this has to do with additional considerations that comes if you have more than one user or more than one data signal that you would like to consider at the same time.

当一个信号到来时，最简单的方式是认为它从某个特定角度射向你的天线阵列，以波前的形式扫过阵列，然后以略微不同的延迟到达各个天线。

So when a signal, it's easiest to think about it, that it comes from a particular angle towards your antenna array, then it arrives as a wavefront that is sort of sweeping over your antenna array, and then it will hit the different antennas with a little bit different delays.

你会在信号的相位差中观察到这一点。

And you will see this in terms of different phase shift in your signals.

如果你希望天线阵列能够区分信号来自哪个方向，或者如何到达你这里，那么关键在于你接收到的是一个连续波，而天线本质上是对这个波进行采样。

And then if you want your antenna array to be able to distinguish between in which directions or how does the signal arrive to you, then it comes down that you're actually having a continuous wave that arrives to you and you have antennas that basically take samples from this.

于是，可以应用奈奎斯特-香农采样定理的经典理论，最终会得出结论：正是λ/2的间距是最优的，因为这样能从信号中获取最多的信息。

And then one could apply classical things from the Nyquist Shannon sampling theorem, and that will eventually come to the conclusion that exactly lambda over two spacing is the best spacing there because then you're sampling your signals so that you the most amount of information out of them.

我明白了，我明白了。

I see, I see.

但现在这假设了一个直视信道，对吧？

But now this assumes a line of sight channel, no?

你刚才的论证假设了用户之间是直视信道。

This argument that you just made assumes a line of sight channel to the users.

这样说准确吗？

Is that accurate to say?

是的，完全正确。

Yes, exactly.

在这种情况下，我讨论的是从不同角度入射的多个平面波，你希望区分它们。

So in that case, I was discussing having some different plane waves coming in from different angles and you want to distinguish between them.

这可能是直视信道，信号从不同方向传来；也可能是一个多径环境，每个平面波都从不同方向入射。

So that could be a line of sight channels, signals coming from different It could potentially be a multipath environment where each plane wave comes in from a different direction as well.

但这种论证可以扩展到多径环境。

But one can extend this kind of argument to a multipath environment.

教科书中最常考虑的情况是我们所说的各向同性散射。

And the most commonly considered situation in textbooks is what we call isotropic scattering.

其理念是用户发送信号后，信号会从大量不同物体上反射，使得信号从各个角度到达天线阵列的概率均等。

The idea is that the user sends a signal and then it bounces on a big variety of objects so that the signal arrives to the antenna array from all angles equally likely.

因此，这只是从不同方向来的平面波的随机组合。

So, it's just a random arrangement of plane waves coming from these different directions.

然后，典型的教科书示例会进一步指出，不同位置的信道特性之间会存在某种数学或统计相关性。

And then the typical textbooks examples then reaches the point that you will have some mathematical or statistical correlation between how the channel looks like at different points.

但如果你将天线恰好放置在半波长的距离上，这种相关性就会为零。

But if you put the antennas exactly half a wavelength apart, that correlation will be zero.

否则，这种相关性被称为sinc函数，它会随着距离增大而减小，这也是一个论点，对的。

And otherwise the correlation is called sinc function is becoming And smaller with that is also an argument, yeah.

是的，我明白了。

Yeah, I see.

所以你的意思是，如果存在各向同性散射，那么衰落系数将会是随机的。

So you're suggesting that if you got an isotropic scattering, then the fading coefficient will be random.

如果你把天线放在相距半波长的两个不同位置上测量衰落系数，那么衰落将是不相关的。

And if you put the antennas, if you measure the fading coefficient at two different points that are half a wavelength apart, then the fading will be uncorrelated.

是的。

Yeah.

所以这听起来是个不错的结果。

So that sounds like a good thing.

我的意思是，到目前为止，我们关心的是不相关的衰落。

I mean, and so far we care about uncorrelated fading.

对。

Yeah.

我意思是，之所以叫衰落，是因为信号质量会上下波动，当然，上升是好事。

And I mean, it's called fading because the signal quality goes up and down, and it's of course good if it goes up.

但糟糕的情况是它下降时，因此为了降低所有天线同时发生这种下降的风险，你希望不同天线上的衰落是不相关或独立的。

But the bad thing is when it fades down, and therefore to minimize the risk that that happens over all of the antennas simultaneously, then you won't like to have this uncorrelated or independent fading on different

最大化阵列的分集增益，或最大化MIMO处理中观察到的信道硬化效果。

maximize the diversity gain of the array or maximize the channel hardening that you see in the MIMO processing.

我的意思是，这变成了一个相当复杂的技術争论，但听起来似乎有一些根本性的原因，使得天线阵列中采用半波长间距是有益的。

I mean this became a rather intricate technical argument, but it sounds like there are some fundamental reasons for why a half a wavelength spacing is good to have in an antenna array.

是的。

Yeah.

无论传播环境如何，因为你提到了视距传播，也提到了各向同性散射，这在某种程度上是视距传播的对立面。

More or less irrespective of the propagation environment, because you mentioned both line of sight here, then you mentioned isotropic scattering which is really the opposite of line of sight in a way.

所以，如果结论是半波长间距实际上非常好，甚至是最优的，那么在我看来，当前的设计实际上已经非常好了。

So now if that's the conclusion that half a wavelength spacing is actually quite good, if not optimal, then it sounds to me that current designs are actually very good.

那么你的新论文是关于什么的呢？

So what is your new paper about that?

对。

Yes.

听起来当前的设计确实很好，因为在这两种非常典型的教科书式例子中，这确实是最佳选择。

It sounds very much as the current designs are good because in these two very textbook like examples, it is the best thing you can do.

因此，人们才一直被这样教导并深信不疑。

So, that's why people have been taught and believed in this.

但问题是，我们在部署基站时所遇到的真实环境，并不完全符合这些不同的例子。

But the thing is that the real environments that we come across when we are deploying our base stations are not exactly matches with any of these different examples.

所以，如果你有直视路径的用户，通常基站是部署在屋顶或塔上，其目的并不是覆盖整个世界，而是覆盖一个约120度的有限区域，也就是世界三分之一的水平范围。

So, if you have line of sight users, it's typically so that a base station is deployed on a rooftop or tower and it's not meant to cover the entire world, but you have a limited sector of some 120 degree where the users are going to be, so one third of the world, and that is horizontally.

而在垂直方向上，所有用户都位于基站下方。

And vertically, all the users are below the base station.

你通常不会有用户在基站上方，这也改变了情况。

You typically don't have users above it, so that is also changing things.

至于多径效应，由于基站通常设置在较高的位置，多径往往发生在用户周围或环境中的一些主要物体上。

And when it comes to the multipaths, since you place your base stations at elevated locations, often the multipaths happens around the user or at some major objects in the environment.

当信号朝基站传播时，并不是从所有角度均匀到达。

And when the signal are arriving towards the base station, it doesn't come uniformly from all angles.

它只从特定的一组角度到达。

It comes from a particular set of angles.

这就形成了一种我们可以利用的结构，从而设计出更能提取这些特定特征的天线阵列。

And this is creating some structure that we can utilize and build arrays that are better at extracting that specific characteristics.

但这确实很有趣。

But that's quite interesting indeed.

我的意思是，你是在暗示基于半波长的天线阵列的这种所谓的最优性或近最优性，只在某些视距场景下成立，或在各向同性散射条件下成立，但现实中我们两者都不具备。

Mean, are you suggesting that this air quotes optimality or near optimality of half wavelength based arrays, well that holds for certain line of sight scenarios, it holds for isotropic scattering, but in practice we have neither of them.

因此，实际上有机会对天线阵列内部的间距进行优化。

And then there is an opportunity to actually optimize the spacing within the array itself.

是的，正是如此。

Yes, exactly.

如果沿用我们之前两个例子中所采用的相同理论方法，但将其应用到这种新情境中，结论将是：为了达到最优，现在你希望天线之间的距离更远一些，用同样的逻辑来推导。

And if one follows the same kind of theoretical practices that we did with those two examples before, but apply to this new situation, the conclusion will be that now you would like the antennas to be further apart, to be optimal using the same kind of arguments.

一旦你决定，好吧，我现在把天线间距设为一个波长，而不是半波长之类的，那么你也就有了不再均匀分布天线的可能性。

And as soon as you say, Okay, now I will put my antennas maybe one wavelength apart instead of half a wavelength apart or something like that, then you also have the possibility of not putting them out uniformly anymore.

因为我们之前说过，你绝不希望间距小于半波长，否则会产生很强的耦合效应。

Because we were saying you never want to be shorter than half a wavelength because then you get a lot of coupling effects.

但如果你能调整天线位置，采用某种非对称布局，同时又避免了互耦问题，为什么不也将其作为设计维度之一呢？

But if you can move them around and have something more asymmetric without running into that mutual coupling problem, why not use that as a design dimension as well?

不，完全正确。

No, absolutely.

百分之百，我的意思是。

100%, I mean.

但即便如此，我认为这可能违背了许多人的直觉，包括我自己，因为如果你有一个孔径，比如说，出于某种原因，我可以负担得起半米的孔径。

But still, I think this might speak against the intuition of a lot of people, including myself, because somehow if you got an aperture, let's say I got I can afford an aperture of half a meter, let's say, for whatever reasons.

可能是由于物理空间、美学原因或其他因素。

Could be that just because of physical space or aesthetic reasons or something else then.

难道我不想尽可能多地在孔径内布置天线吗？

Wouldn't I wanna fill this aperture with as many antennas as possible.

而既然我们知道，不希望把天线放得比半波长更近，但我仍然希望尽可能填满整个孔径。

And then since we know that, we don't want to put antennas closer than half a wavelength together, but I still want to fill the aperture as much as possible.

因此，这意味着要尽可能多地排列天线。

And from that it would follow that packing as many as possible.

也就是说，半波长的间距。

That means half a wavelength spacing.

对，这说得通

Yeah, that makes a

很有道理。

lot of sense.

但问题在于，这么做还会牵扯到成本、重量、体积这些相关的问题。

But the problem is that it is also associated with cost and weight and bulkiness and things like that.

你之前还提到，实际上5G基站可能会配备128个阵列单元，但我们只会说它有64或32根天线。

So you were mentioning earlier that actually a five gs base station might have 128 elements, but we only say that it has 64 or 32 antennas.

而正是出于这个原因，如果你加装足够多的无线电硬件，以便单独控制每一个单元，那整个设备的成本、重量和体积都会增加。

And that is exactly for this reason that if you would put in enough radio hardware so you can control every element individually, you would increase the cost and the weight and bulkiness of the whole thing.

所以业内已经开始研究如何在这些方面做出恰当的权衡了。

So they have already started to play with the right kind of trade offs there.

那我之前就在想，在6G系统里，如果只是单纯扩容，把天线数量增加个四五倍，那设备的体积也会跟着变大。

And now I was thinking about in a six gs system, if you would just scale things up and have some four, five, six times more antennas, then the bulkiness will grow as well.

或许我们可以利用天线阵列的这种非均匀排布，用更少的天线实现相近的性能，比如说把天线的使用量从4到8个缩减到2个左右。

And maybe we could utilize this non uniformity in the arrays so that we can get similar performance, but with a little bit fewer antennas, maybe cut down on this antenna user from four or eight to two or something like that.

是的，但这还挺酷的。

Yeah, but it's kind of cool.

现在真正的问题是：给定一个孔径尺寸、系统的可接受成本以及天线数量的上限或最大值，如何在该孔径内最佳地布置这些天线？

It's really the design problem now is that, okay, given an aperture size and given a permissible cost of the system and given a permissible or maximum number of antennas, what is the best way to place them within this aperture?

而半波长间距甚至可能不可行，因为我们没有足够的天线来实现半波长间距。

And then lambda half spacing might not even be an option because we don't have enough antennas to put them with lambda half spacing.

所以我们不得不让天线间距更稀疏，或者非均匀、随机地布置等等。

So we got to put them either more sparsely apart or non uniformly or randomly or something.

那么你是在说，这实际上是一个我们可以解决的优化问题。

Then you're suggesting that here is actually an optimization problem that we can solve.

没错。

Exactly.

甚至对于传播环境也是如此。

Even for propagation environment.

那我们就往这个方向深入探讨吧。

So let's go there.

如果我们这样做，将天线非均匀地分布在孔径上，波束模式会是什么样子？

Now if we do this, so we put the antennas non uniformly over an aperture, what are the beam patterns going to look like?

对。

Right.

如果有人打开一本教科书，说我们来构建一个天线间距大于半波长的均匀阵列，会发生什么？

So if one opens a textbook and say, let's build a uniform array, but with an antenna spacing that is larger than half a wavelength, what is going to happen?

总的孔径长度，也就是最外侧天线之间的距离，决定了信号的窄度。

Well, the total aperture length, so distance between the outermost antennas, that is determining how narrow the signal is going to be.

所以当你发射波束时，它可能呈圆锥形，而这个形状的半径由阵列的长度决定。

So you shoot the beam, it has a perhaps cone like shape and the radius of that shape is determined by how long the array is.

阵列越长，波束就越窄。

So longer it is, the more narrow it becomes.

但因为你仍然要发送总功率，所以能量必须有个去处。

But since you still have a total amount of transmit power that you're sending out, then it needs to go somewhere.

所以如果你更精确地将波束对准接收器，就会有一些泄漏方向，这些方向也会呈现出某种形状。

So if you aim it in a more sharp way towards your receiver, then there will also be some leakage directions, and that one is having some kind of shape.

信号越窄，尤其是在稀疏阵列且间距大于半波长时，这些被称为旁瓣的其他方向上的旁瓣就会变得更大，并且还可能出现栅瓣现象。

And the more narrow the signal is, the more in particular when you have a sparse array, larger than lambda over two spacings, the side lobes as these other directions are called, becomes larger and there is a concept of grating lobes that could also happen.

这些旁瓣与你希望发射信号的方向难以区分。

These are side lobes that are indistinguishable from the direction where you would like to transmit.

所以你朝一个方向发射，却在另一个方向上也产生了同样强度的信号。

So you send in one direction and then you have an equally strong signal going in another direction.

是的。

Sure.

所以你基本上是说，如果我们从半波长间距的均匀线性阵列开始，然后像拉伸孔径一样扩大它。

So basically what you're saying is that fundamentally, let's say that we start with half and half a wavelength spaced uniform linear array, and then we of like we stretch the aperture.

好的。

Okay.

当然，我们无法保持天线之间的间距，但我们会拉伸孔径，然后将天线大致随机地放置在这个扩展后的孔径内。

And then of course we can't maintain the spacing between the antennas, but we stretch the aperture, and then we just place the antennas a bit kind of at random within that aperture that we have gotten.

一般来说，此时的间距会大于半波长。

In general then the spacing will be larger than half a wavelength.

那么会发生的是，你的波束成形中的主瓣幅度不会改变，因为它始终等于你的M2功率。

Then what will happen is that, well, the main lobe in your beamforming, the magnitude of the main lobe will not change, because it's always equal to your M2 in power.

但这个主瓣会变窄，因为孔径变大了。

But that main lobe will get narrower, because the aperture is larger.

但为此你也会产生旁瓣，即指向其他随机方向的栅瓣，这可能会很糟糕，因为可能有某个人无意中被你干扰了。

But to pay for that you also get side lobes, the grading lobes that point in other random directions, which could be bad of course because there could be somebody out there whom you're shooting interference at inadvertently.

但这真的重要吗？

But does this really matter?

我的意思是，我们在栅瓣问题上纠结，是因为在所有的MIMO理论中，我们知道使用最大比波束成形时，只有天线数量和路径损耗才重要。

I mean, we're grading lobes because in all the MIMO theory we know that with, let's say, maximum radio beamforming, then it's only the number of antennas and the path loss that matters.

对于多用户波束成形，我们通常只是用随机统计信道模型来评估性能。

For multiuser beamforming, a lot of times we just evaluate performance on random statistical channel models.

这些栅瓣在实际中会产生影响吗？

Will these grating lobes make a difference in practice?

对。

Right.

我以为其实不会。

I thought not really.

这当然取决于你所处的传播环境和具体情况。

It certainly depends on what kind of propagation environment you have and the situation there.

所以你可能会遇到一种不幸的情况，栅瓣恰好朝向另一个用户的位置，从而造成大量干扰。

So you could be in an unlucky situation where the grating lobe creates a lot of interference aiming accidentally exactly towards where another user is located.

然后你就面临一个问题：你该怎么办？

And then you come into a situation where what what should you do?

你要么不向目标用户发送太多信号，要么造成大量干扰。

Either you don't transmit very much to your intended user or you create a lot of interference.

你该如何应对这类情况？

How do you deal with those kinds of situations?

我认为在单小区场景中，只有一个基站和几个用户时，你仍然可以处理干扰问题。

And I would say that in a single cell situation, you only have one base station and a couple of users, you can still deal with interference.

你对一切都有控制权。

You are in control of everything.

你可以调整波束，以应对其中一些问题。

You can tune your beams so that you might be dealing with some of these issues.

但人们通常在天线阵列设计中关注栅瓣，因为这可能会对其他小区或周围系统造成干扰，或者如果你正在设计也将用于到达角估计的阵列，你希望定位信号的来源，以帮助谷歌地图或其他应用告诉你用户的位置，那么如果信号看起来既可能是这个方向，也可能是另一个方向，就会出现问题。

But people are usually concerned with grating lobes in array design because it is either bad for sort of interference that you're hitting some other cells or other systems around, or if you are building arrays that are also going to be used for so called angle of arrival estimation, you would like to localize from where did the signal come to aid some Google Maps or some other application to sort of tell you where is the user, then it's problematic if it's either this direction or it could have been this other direction that it looks the same.

这一切都归结为我们之前讨论过的采样定理。

And this all comes down to the sampling theorem that we talked about earlier.

熟悉这一点的人知道，如果在时间上采样过于稀疏，就会有多个信号看起来完全相同。

People who are familiar with that one knows that if you sample too sparsely in time, then there are multiple signals that looks the same.

它们彼此是混叠信号。

They are the aliases of each other.

如果在空间上采样间隔过远，也会发生同样的情况。

The same thing happens if you're sampling in space too far apart.

来自不同角度的信号，你实际上无法区分。

There are signals coming from different angles that you actually can't tell apart.

当然，关于到达角估计，我完全同意。

Sure, 100% on the angle of arrival estimation.

我的意思是，旁瓣会严重影响你的模糊函数，这可能会很糟糕。

I mean, having grading lobes racks your ambiguity function, that can be pretty bad.

但从通信的角度来看，结合空间复用和波束成形，我觉得这些旁瓣未必那么严重，因为虽然你会产生旁瓣，但同时也获得了更窄的主瓣，这意味着其他人非常接近你的目标用户并落入同一主瓣的可能性也会降低。

But from a communications perspective with spatial multiplexing and beamforming, it seems to me that these grating lobes aren't necessarily that much of a big deal because, I mean, you do get the grating lobes, but you also get a narrower main lobe, which means that the likelihood that somebody else is very close to your targeted user and would fall in the same main lobe, that chance also deduces.

所以这里存在一个复杂的权衡：你可能会在某些随机方向上造成一些干扰，但同时也显著减少了在目标用户附近方向上的干扰。

So there's a complicated trade off here between, you know, you might create some interference in some other random direction, but you're certainly also creating less interference in directions that are very close to where your targeted user lies.

对。

Right.

但接下来有趣的是，当你将天线阵列拉伸到某一特定长度时，决定主瓣有多窄、聚焦能力有多强的，是外侧天线之间的距离。

But here comes the interesting thing then, that when you have stretched your arrays out to a particular length, it is the distance between the outermost antennas that determines how narrow your main lobe, your focusing is.

但内部天线的确切位置也很重要。

But the exact location of the antennas at the inside matters as well.

它们会影响非主方向上的波束图案形态。

And they matter in terms of deciding how does the pattern look like in directions that are not the main direction.

因此，如果天线是均匀但稀疏部署的，就会产生旁瓣；但如果采用其他布局，信号图案就会有所不同。

So, if they are exactly uniformly but sparsely deployed, you get this grating But lobe if they have some other shape, you can get a different shape of the signals.

如果你以正确的方式调整天线的位置，可能会使主瓣以外的信号几乎均匀地分布在所有其他角度上，这对系统可能是有益的。

And if you are tuning the locations of the antennas in the right way, you might actually get that the signal that are not in the main lobe are spread almost uniformly over all of the other angles, and that can be beneficial for a system.

完全正确。

Totally.

我认为这是一个非常重要的观点，即主瓣的宽度主要由孔径的大小决定，也就是最左端和最右端天线之间的距离。

I think that's a very important point indeed that the width of the main lobe is chiefly determined by the extent of the aperture, so the distance between the leftmost and the rightmost antenna.

而栅瓣图案的出现则取决于位于最左端和最右端天线之间所有天线的排列方式。

Whereas the appearance of the grating lobe pattern will depend on the arrangement of all the antennas that lie in between the leftmost and the rightmost.

那么，这是缓解栅瓣的方法吗？

So is that the way to mitigate grading lobes?

既然栅瓣本身可能是个问题，那么缓解它们的方法是不是只是在孔径内随机放置天线？

Now insofar grading lobes are a problem to start with, is the way to mitigate them to just place the antennas randomly within within the aperture?

还是说有其他可以采取的措施？

Or is there something else that one could do?

你可以随机分布天线，这样就会产生一些不太可能具有特定栅瓣的其他模式。

So you could put them out randomly and then you get some other patterns that are unlikely to have specific grating lobes.

如果你将这个定义为一个与主瓣强度相同的旁瓣方向，那么这种情况很可能不会发生。

If you define this as a beam direction that is a side lobe and equally strong as your main lobe, well then that will most likely not happen.

但你实际上可以设计天线的位置并进一步优化它们。

But you can actually design the antenna locations and optimize them even further.

长期以来，人们在太空观测情境中一直研究这个问题。

And people have been studying this for a long time in space observation situations.

这是一种你部署大型天线对准天空的情况，你可能会在远离城市的区域找到几乎没有电磁干扰的地方。

So this is a situation where you put out big antennas that you aim towards the sky and you might find some area far from the cities where there will not be much electromagnetic interference from anything.

在部署设备所用的土地面积方面，你并没有受到太多限制。

You're not really constrained in terms of the land area where you can deploy things.

你只是受限于能部署多少天线。

You're just constrained about how many antennas you can put out there.

在那里，人们已经研究了五十多年，如何布置天线，以便能够观测到来自太空不同方向的信号，同时抑制旁瓣或栅瓣。

And there people started to analyze for more than fifty years how to position the antennas so that you could sort of see things coming from different directions in space, but still mitigating the side lobes or these grating lobes.

当然。

Sure.